Dirty air: The federal government has enacted maximum allowable standards for air pollutants such as ozone. Let X be the number of days per year that the level of air pollution exceeds the standard in a certain city. The probability distribution of X is given by Xx P(x) Part: 0 / 2 Part 1 of 2 μx (a) Compute the mean ux. Round the answer to three decimal places as needed. = Part: 1 / 2 Part 2 of 2 ox 0 0.33 1 2 3 4 0.36 0.17 0.1 0.04 (b) Compute the standard deviation ox. Round the answer to three decimal places as needed. = X
Dirty air: The federal government has enacted maximum allowable standards for air pollutants such as ozone. Let X be the number of days per year that the level of air pollution exceeds the standard in a certain city. The probability distribution of X is given by Xx P(x) Part: 0 / 2 Part 1 of 2 μx (a) Compute the mean ux. Round the answer to three decimal places as needed. = Part: 1 / 2 Part 2 of 2 ox 0 0.33 1 2 3 4 0.36 0.17 0.1 0.04 (b) Compute the standard deviation ox. Round the answer to three decimal places as needed. = X
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Dirty Air: Analyzing Air Pollution Exceedance**
The federal government has set maximum allowable standards for air pollutants such as ozone. In this scenario, let \( X \) represent the number of days per year that air pollution levels surpass these standards in a particular city. The probability distribution of \( X \) is provided in the table below:
\[
\begin{array}{c|ccccc}
x & 0 & 1 & 2 & 3 & 4 \\
\hline
P(x) & 0.33 & 0.36 & 0.17 & 0.10 & 0.04 \\
\end{array}
\]
**Part 1 of 2**
(a) *Calculate the Mean (\( \mu_X \)):*
To find the mean of \( X \), compute the expected value as follows:
\[
\mu_X = \sum (x \cdot P(x))
\]
Round your final answer to three decimal places.
**Part 2 of 2**
(b) *Calculate the Standard Deviation (\( \sigma_X \)):*
To determine the standard deviation, calculate:
\[
\sigma_X = \sqrt{\sum [(x - \mu_X)^2 \cdot P(x)]}
\]
Again, round your answer to three decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe67a4001-a6ff-4bd3-8f91-ff24e2266284%2F2b7c2528-34cf-439a-9135-d5de8d5c36c5%2Fuu4e37d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Dirty Air: Analyzing Air Pollution Exceedance**
The federal government has set maximum allowable standards for air pollutants such as ozone. In this scenario, let \( X \) represent the number of days per year that air pollution levels surpass these standards in a particular city. The probability distribution of \( X \) is provided in the table below:
\[
\begin{array}{c|ccccc}
x & 0 & 1 & 2 & 3 & 4 \\
\hline
P(x) & 0.33 & 0.36 & 0.17 & 0.10 & 0.04 \\
\end{array}
\]
**Part 1 of 2**
(a) *Calculate the Mean (\( \mu_X \)):*
To find the mean of \( X \), compute the expected value as follows:
\[
\mu_X = \sum (x \cdot P(x))
\]
Round your final answer to three decimal places.
**Part 2 of 2**
(b) *Calculate the Standard Deviation (\( \sigma_X \)):*
To determine the standard deviation, calculate:
\[
\sigma_X = \sqrt{\sum [(x - \mu_X)^2 \cdot P(x)]}
\]
Again, round your answer to three decimal places.
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